Follow path not align on the path
You are doing it the wrong way:


delete the parent relationship, you won't need it
create a Follow Path constraint on the object and select the curve in the Target field





As you can see the origin of the object is on the curve, but the object itself is not, so to fix it, with the objects selected, go to Object > Set Origin > Origin to Center of Mass (Surface), and press Alt + G to reset the object's position





You may want to enable Curve Radius in the constraint




NOTE

In your picture, unlike in your .blend file, you have many of those object on the curve. If you want multiple copies of the object on the curve you should use an Array Modifier with a Curve Modifier